# Help Math

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A circular pulley with a radius of 10 cm is turning at 12 revolutions per minute. How
fast is a point on the edge of the pulley rising when it is 5 cm higher than the center of
the pulley?

• Help Math -

Draw a diagram. Consider point P on the circle, at height h above the center of the pulley. Let the radius from the center to P make angle θ with the horizontal.

h/r = sinθ

since r = 10,

h = 10 sinθ
dh/dt = 10 cosθ dθ/dt

Since the wheel is turning at 12 rpm, dθ/dt = 24π/min

dh/dt = 10 * √3/2cm * 24π/min = 653 cm/min

• Help Math -

Thanks Steve

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